You may be able to depending on the clutch... My Exedy Twin vibrates audibly on engagement and can be felt, though that may be through the chassis into the pedal assembly.

Aggressively launching the car can also create clutch vibrations that can be felt, again though likely through the chassis. A stiffer chassis will definitely transmit these more than something commuter-y, but at the same time so can worn components, such as motor mounts, where you're feeling the motor move, not the clutch.